--- title: "Negative Correlation | Intro to Statistics" description: "Negative correlation in Intro to Statistics means two quantitative variables move in opposite directions, a pattern you read from scatter plots and r values." canonical: "https://fiveable.me/college-intro-stats/key-terms/negative-correlation" type: "key-term" subject: "Intro to Statistics" unit: "Unit 12" --- # Negative Correlation | Intro to Statistics ## Definition Negative correlation is a relationship in Intro to Statistics where one quantitative variable tends to go down as the other goes up. On a scatter plot, the points slope downward from left to right, and the correlation coefficient is negative. ## What It Is Negative correlation in Intro to Statistics is a pattern where two quantitative variables move in opposite directions. If one variable increases, the other tends to decrease. If one decreases, the other tends to increase. The quickest way to spot it is on a scatter plot. A cloud of points with a downward trend from left to right usually signals a negative association. For example, if x represents price and y represents demand, higher prices often line up with lower demand, which creates a negative pattern. The sign of the correlation coefficient tells you the direction. A negative r means the variables move in opposite directions. The value itself still matters, though, because the strength is shown by how close r is to -1. A correlation of -0.85 shows a much stronger negative linear relationship than -0.20. One common mistake is thinking a negative correlation means something bad or harmful. In statistics, negative just describes direction, not quality. It does not mean one variable causes the other to fall, and it does not mean the relationship is weak. A very strong negative correlation can exist, especially when the points cluster closely around a downward-sloping line. Another thing to watch for is linearity. Negative correlation usually refers to a linear downward pattern, not just any relationship where one variable eventually drops as the other rises. If the scatter plot curves, the variables may still be related, but a simple correlation coefficient may not describe that relationship well. In Intro to Statistics, you usually pair the visual pattern with the numerical r value before deciding how to describe the association. A compact example is study time and number of mistakes on a quiz. As study time increases, mistakes often decrease. That does not guarantee perfect data, since real data have scatter, but the overall slope can still be negative. ## Why It Matters Negative correlation shows up everywhere in Intro to Statistics because you are constantly comparing two quantitative variables and deciding what kind of association they have. If you can read the direction correctly, you can describe a scatter plot more precisely instead of just saying two variables are “related.” It also helps you avoid mixing up direction and strength. A weak negative correlation and a strong negative correlation both point downward, but they do not tell the same story. One may look loosely scattered, while the other hugs a line more tightly. That difference matters when you write about data, interpret a graph, or decide whether a linear model fits. This term connects directly to correlation and regression. Once you recognize a negative pattern, you can think about whether a trend line should slope downward and whether predictions should decrease as x increases. That shows up in homework, lab reports, and any problem where you interpret a graph of paired data. It also trains you to be careful about causation. A negative correlation can be real without one variable causing the other. In statistics, that distinction matters a lot, especially when the data come from observation rather than a controlled experiment. ## Connections ### Correlation Coefficient The correlation coefficient, written as r, tells you both direction and strength. A negative value means the association is negative, and the closer r is to -1, the tighter the linear pattern. If you only look at the sign, you miss how strong the relationship really is. ### Scatter Plot A scatter plot is usually where you first notice negative correlation. The points slope downward from left to right when larger x-values tend to match smaller y-values. This visual check matters because r should match the pattern you can actually see in the graph. ### Linear Regression Linear regression can model a negative correlation with a line that slopes downward. If the relationship is fairly linear, the regression line gives you a way to predict y from x. The negative slope tells you the predicted y-value drops as x increases. ### [Nonlinear Relationship](/college-intro-stats/key-terms/nonlinear-relationship) Not every relationship with opposite movement is a negative correlation. If the points bend into a curve, the relationship may be negative in part of the graph but not well described by a single correlation coefficient. That is why you check the shape, not just the direction. ## On the AP Exam A quiz or problem set question may show you a scatter plot and ask whether the relationship is positive, negative, or none. You answer negative correlation when the points slope downward from left to right. If the question gives you r, a negative number tells you the direction, and the size of the number helps you judge strength. You may also need to explain the relationship in words, such as “as x increases, y tends to decrease.” That wording is safer than claiming a perfect pattern. If the plot is messy but still trends downward, describe it as a negative association rather than pretending every point follows the same rule. For written responses, be ready to separate correlation from causation. You can say two variables are negatively correlated without saying one causes the other to change. That distinction is a common point of feedback in Intro to Statistics assignments. ## Negative Correlation vs Positive Correlation Positive correlation is the opposite direction, where both variables tend to increase or decrease together. Negative correlation means one goes up while the other goes down. Students often mix them up on scatter plots, so check the slope of the point pattern before naming the relationship. ## Key Takeaways - Negative correlation means two quantitative variables move in opposite directions. - A scatter plot with a downward trend from left to right usually shows negative correlation. - The sign of r tells direction, and the distance from -1 tells you how strong the linear relationship is. - Negative correlation does not mean bad, and it does not prove that one variable causes the other. - Always check whether the pattern looks roughly linear before you rely on correlation. ## FAQs ### What is negative correlation in Intro to Statistics? Negative correlation is a relationship between two quantitative variables where one tends to increase as the other decreases. In Intro to Statistics, you usually spot it on a scatter plot that slopes downward from left to right. The correlation coefficient r is negative when the relationship has this direction. ### How do you tell if a scatter plot has negative correlation? Look for a downward pattern as you move from left to right. If higher x-values tend to line up with lower y-values, the plot shows negative correlation. A loose downward cloud is still negative, even if the points are not perfect. ### What does a negative correlation coefficient mean? A negative correlation coefficient means the two variables move in opposite directions. The closer the coefficient is to -1, the stronger the negative linear relationship. A value near 0 means the linear relationship is weak, even if the sign is negative. ### Is negative correlation the same as causation? No. Two variables can be negatively correlated without one causing the other to change. In statistics, you need the study design and context before making a causal claim. Correlation only describes association. ## Related Study Guides - [12.2 Scatter Plots](/college-intro-stats/unit-12/2-scatter-plots/study-guide/7liioHpD5EDRt0V7) ## About This Document Canonical Fiveable pages are available as Markdown at the same path plus `.md`. - [llms.txt](https://fiveable.me/llms.txt): index of Fiveable's sections and URL patterns - [llms-full.txt](https://fiveable.me/llms-full.txt): complete subject and unit listing - [MCP server](https://fiveable.me/mcp): call Fiveable as tools instead of fetching pages (`https://fiveable.me/api/mcp`) - [MCP server for AP teachers](https://fiveable.me/mcp/teachers): a teacher's classes, assignments and AP-rubric grading (`https://fiveable.me/api/mcp/teacher`) ## Structured Data ```json {"@context":"https://schema.org","@graph":[{"@type":"LearningResource","@id":"https://fiveable.me/college-intro-stats/key-terms/negative-correlation#resource","name":"Negative Correlation | Intro to Statistics","url":"https://fiveable.me/college-intro-stats/key-terms/negative-correlation","learningResourceType":"Concept explainer","educationalLevel":"AP® / High School","about":{"@id":"https://fiveable.me/college-intro-stats/key-terms/negative-correlation#term"},"audience":{"@type":"EducationalAudience","educationalRole":"student"},"dateModified":"2026-07-03T02:21:06.614Z","isPartOf":{"@type":"Collection","name":"Intro to Statistics Key Terms","url":"https://fiveable.me/college-intro-stats/key-terms"},"author":{"@type":"Organization","@id":"https://fiveable.me/editorial#content-team","name":"Fiveable Content Team","url":"https://fiveable.me/editorial","parentOrganization":{"@id":"https://fiveable.me/#organization"},"member":[{"@type":"Person","name":"Amanda DoAmaral","sameAs":["https://www.linkedin.com/in/adoamaral"]},{"@type":"Person","name":"Becky Bahr","sameAs":["https://www.linkedin.com/in/becky-bahr-b52743132"]}]},"publisher":{"@type":"Organization","name":"Fiveable","url":"https://fiveable.me"}},{"@type":"DefinedTerm","@id":"https://fiveable.me/college-intro-stats/key-terms/negative-correlation#term","name":"Negative Correlation","description":"Negative correlation is a relationship in Intro to Statistics where one quantitative variable tends to go down as the other goes up. 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